## Gibbard's theorem |

in the fields of

andmechanism design ,social choice theory **gibbard's theorem**is a result proven by philosopher in 1973.allan gibbard ^{[1]}it states that for any deterministic process of collective decision, at least one of the following three properties must hold:- the process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome;
- the process limits the possible outcomes to two options only;
- the process encourages agents to think strategically: once an agent has identified their preferences, they have no action at their disposal that would best defend their opinions in any situation.

a corollary of this theorem is

about voting rules. the main difference between the two is that gibbard–satterthwaite theorem is limited togibbard–satterthwaite theorem : a voter's action consists in giving a preference ranking over the available options. gibbard's theorem is more general and considers processes of collective decision that may not be ordinal: for example, voting systems where voters assign grades to candidates.ranked (ordinal) voting rules gibbard's theorem is itself generalized by gibbard's 1978 theorem and hylland's theorem, which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve a part of chance.

- overview
- formal statement
- examples
- notes and references
- see also

In the fields of **Gibbard's theorem** is a result proven by philosopher ^{[1]} It states that for any deterministic process of collective decision, at least one of the following three properties must hold:

- The process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome;
- The process limits the possible outcomes to two options only;
- The process encourages agents to think strategically: once an agent has identified their preferences, they have no action at their disposal that would best defend their opinions in any situation.

A corollary of this theorem is

Gibbard's theorem is itself generalized by Gibbard's 1978 theorem and Hylland's theorem, which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve a part of chance.